2. Adequate sets of connectives For this question, we introduce two new connectives, NAND and XOR. For a truth as- signment v, we define the truth values of two new connectives as follows: v(p NAND q) is true if and only if v(p) and v(q) are not both true at the same time, and v(p XOR q) is true if and only v(p)v(q). See also the truth tables for NAND and XOR below. p (p NAND q) | (p XOR TIF F T FIF (a) Prove that (NAND) is an adequate set of connectives (that is, NAND is adequate on its own!) (b) Prove tat (XOR is not an adequate set of connectives